Easter Bread (Tsoureki)

Place 5 or 6 eggs in a medium pot. Pour in cold water to cover by 1" and bring to a boil over medium-high heat. Remove from heat, cover pot, and let stand for 10 minutes. Transfer eggs to a medium bowl of ice water; let cool completely.
If desired, color eggs according to food-coloring package directions. Transfer eggs to paper towels to dry. DO AHEAD: Eggs can be dyed up to 1 week ahead. Cover and chill.
Line a large baking sheet with parchment paper. Punch down dough. Divide into 3 equal pieces. With lightly floured hands, roll each piece on a lightly floured surface into a 16"- long rope with tapered ends. (If dough begins to bounce back, cover with a kitchen towel and let rest for 10 minutes to allow dough to relax.)
Arrange ropes side by side lengthwise on prepared sheet. Pinch top ends together. Braid dough. Pinch bottom ends together to secure (braided loaf will be about 12" long). Tuck dyed eggs between braids, spacing evenly. Loosely cover with plastic wrap or a kitchen towel. Let rise in a warm, draft-free area until puffed but not doubled in size, 45-50 minutes. Arrange a rack in middle of oven; preheat to 375°F. Whisk remaining egg with 2 teaspoons warm water in a small bowl. Avoiding dyed eggs, brush dough all over with egg wash. Bake until bread is golden and an instantread thermometer inserted into center of loaf registers 190°F, 20-25 minutes. Let cool on a wire rack. Serve warm or at room temperature. DO AHEAD: Can be made 8 hours ahead. Let cool completely and store airtight at room temperature.